## A Weyl-Titchmarsh type formula for a discrete Schrödinger operator with Wigner-von Neumann potential.(English)Zbl 1205.47029

Summary: We consider a discrete Schrödinger operator $$\mathcal J$$ with Wigner-von Neumann potential not belonging to $$l^2$$. We find the asymptotics of orthonormal polynomials associated to $${\mathcal J}$$. We prove a Weyl-Titchmarsh type formula, which relates the spectral density of $${\mathcal J}$$ to a coefficient in the asymptotics of the orthonormal polynomials.

### MSC:

 47B36 Jacobi (tridiagonal) operators (matrices) and generalizations 34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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